R-equivalence and rationality problem for semisimple adjoint classical algebraic groups
Merkurjev, Alexander S.
Publications Mathématiques de l'IHÉS, Tome 84 (1996), p. 189-213 / Harvested from Numdam
@article{PMIHES_1996__84__189_0,
     author = {Merkurjev, Alexander S.},
     title = {R-equivalence and rationality problem for semisimple adjoint classical algebraic groups},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {84},
     year = {1996},
     pages = {189-213},
     mrnumber = {98d:14055},
     zbl = {0884.20029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1996__84__189_0}
}
Merkurjev, Alexander S. R-equivalence and rationality problem for semisimple adjoint classical algebraic groups. Publications Mathématiques de l'IHÉS, Tome 84 (1996) pp. 189-213. http://gdmltest.u-ga.fr/item/PMIHES_1996__84__189_0/

[1] A. A. Albert, Tensor products of quaternion algebras, Proc. Amer. Math. Soc., 35 (1972), 65-66. | MR 45 #6855 | Zbl 0263.16012

[2] H. P. Allen, Hermitian forms II, J. Algebra, 10 (1968), 503-515. | MR 39 #237 | Zbl 0302.15031

[3] J. Arason, Cohomologische Invarianten quadratischer Formen, J. Algebra, 36 (1975), 448-491. | MR 52 #10592 | Zbl 0314.12104

[4] E. Bayer, D. B. Shapiro, J.-P. Tignol, Hyperbolic Involutions, Math. Z., 214 (1993), 461-476. | MR 94j:16060 | Zbl 0796.16029

[5] A. Borel, T. A. Springer, Rationality properties of linear algebraic groups II, Tôhoku Math. J., 20 (1968), 443-497. | MR 39 #5576 | Zbl 0211.53302

[6] V. I. Černousov, The group of multipliers of the canonical quadratic form and stable rationality of the variety PSO (in Russian), Matematicheskie zametki, 55 (1994), 114-119. | Zbl 0855.11019

[7] C. Chevalley, On algebraic group varieties, J. Math. Soc. Jap., 6 (1954), 303-324. | MR 16,672g | Zbl 0057.26301

[8] J.-L. Colliot-Thélène, J.-J. Sansuc, La R-équivalence sur les tores, Ann. scient. Éc. Norm. Sup., 4e série, 10 (1977), 175-230. | Numdam | MR 56 #8576 | Zbl 0356.14007

[9] M. Demazure, A. Grothendieck, Schémas et Groupes III (SGA 3, t. III), Lecture Notes in Math., No. 153, Springer, Heidelberg, 1970. | Zbl 0212.52810

[10] J. Dieudonné, Sur les multiplicateurs des similitudes, Rend. Circ. Mat. di Palermo, 3 (1954), 398-408. | MR 17,236b | Zbl 0057.25201

[11] R. Elman, T.-Y. Lam, Quadratic forms under algebraic extensions, Math. Ann., 219 (1976), 21-42. | MR 53 #5476 | Zbl 0302.10025

[12] P. Gille, R-équivalence et principe de norme et cohomologie galoisienne, C. R. Acad. Sci. Paris, 316 (1993), 315-320. | MR 94a:12010 | Zbl 0826.12003

[13] N. Jacobson, Clifford algebras for algebras with involution of type D, J. Algebra, 1 (1964), 288-300. | MR 29 #5849 | Zbl 0135.07401

[14] M.-A. Knus, Quadratic and Hermitian Forms over Rings, Grundlehren math. Wiss., 294, Berlin, Springer-Verlag, 1991. | MR 92i:11039 | Zbl 0756.11008

[15] M.-A. Knus, A. S. Merkurjev, M. Rost, J.-P. Tignol, Book of involutions, in preparation. | Zbl 0955.16001

[16] M.-A. Knus, R. Parimala, R. Sridharan, Involutions on rank 16 central simple algebras, J. Indian Math. Soc., 57 (1991), 143-151. | MR 93c:16020 | Zbl 0824.16017

[17] M.-A. Knus, R. Parimala, R. Sridharan, On the discriminant of an involution, Bull. Soc. Math. Belgique, Sér. A, 43 (1991), 89-98. | MR 95m:16009 | Zbl 0757.12002

[18] T.-Y. Lam, The Algebraic Theory of Quadratic Forms, Benjamin, Reading, Massachusetts, 1973. | MR 53 #277 | Zbl 0259.10019

[19] D. Lewis, J.-P. Tignol, Square class groups and Witt rings of central simple algebras, J. Algebra, 154 (1993), 360-376. | MR 94a:19007 | Zbl 0766.11024

[20] Yu. I. Manin, Cubic forms, Amsterdam, North-Holland, 1974. | Zbl 0277.14014

[21] A. S. Merkurjev, Simple algebras and quadratic forms, Math. USSR Izvestia, 38 (1992), 215-221. | MR 93b:16025 | Zbl 0763.12003

[22] A. S. Merkurjev, Generic element in SK1 for simple algebras, K-theory, 7 (1993), 1-3. | MR 94g:19001 | Zbl 0811.16011

[23] A. S. Merkurjev, Involutions and algebraic groups, Preprint. Recherches de mathématique, No. 36, Université catholique de Louvain, Louvain-la-Neuve, Belgium (1993).

[24] A. S. Merkurjev, I. A. Panin, A. Wadsworth, Index reduction formulas for twisted flag varieties, I, K-theory, 10 (1996), 517-596. | MR 98c:16018 | Zbl 0874.16012

[25] A. S. Merkurjev, A. A. Suslin, K-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Math. USSR Izvestiya, 21 (1983), 307-340. | Zbl 0525.18008

[26] A. S. Merkurjev, J.-P. Tignol, The multipliers of similitudes and the Brauer group of homogeneous varieties, J. reine angew. Math., 461 (1995), 13-47. | MR 96c:20083 | Zbl 0819.16015

[27] V. P. Platonov, Algebraic groups and reduced K-theory, Proc. Inter. Congr. Math., V.1. Helsinki, 1978, p. 311-317. | MR 81h:12017 | Zbl 0425.16018

[28] V. P. Platonov, On the problem of rationality of spinor varieties, Soviet Math. Dokl., 20 (1979), 1027-1031. | MR 81a:14027 | Zbl 0435.20028

[29] V. P. Platonov, V. I. Čhernousov, On the rationality of canonical spinor varieties, Soviet Math. Dokl., 21 (1980), 830-834. | MR 81k:14019 | Zbl 0486.14013

[30] J.-J. Sansuc, Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres, J. reine angew. Math., 327 (1981), 12-80. | MR 83d:12010 | Zbl 0468.14007

[31] W. Scharlau, Quadratic and Hermitian Forms, Grundlehren math. Wiss., 270, Berlin, Springer-Verlag, 1985. | MR 86k:11022 | Zbl 0584.10010

[32] A. Schofield, M. Van Den Bergh, The index of a Brauer class on a Brauer-Severi variety, Trans. Amer. Math. Soc., 333 (1992), 729-739. | MR 92m:12003 | Zbl 0778.12004

[33] D. Tao, The generalized even Clifford algebra, J. Algebra, 172 (1995), 184-204. | MR 96e:15051 | Zbl 0837.16032

[34] J.-P. Tignol, Algèbres indécomposables d'exposant premier, Advances in Math., 65 (1987), 205-228. | MR 88h:16028 | Zbl 0642.16015

[35] J.-P. Tignol, A Cassels-Pfister theorem for involutions on central simple algebras, J. Algebra, 181 (1996), 857-875. | MR 97e:16043 | Zbl 0847.16019

[36] J. Tits, Formes quadratiques, groupes orthogonaux et algèbres de Clifford, Invent. Math., 5 (1968), 19-41. | MR 37 #6307 | Zbl 0155.05202

[37] J. Tits, Classification of algebraic semisimple groups, in Algebraic Groups and Discontinuous Subgroups (A. BOREL and G. D. MOSTOV, eds), Proc. Symp. Pure Math., IX, Providence, Amer. Math. Soc., 1966, p. 32-62. | MR 37 #309 | Zbl 0238.20052

[38] V. E. Voskresenskiĭ, Algebraic tori, Nauka, Moscow, 1977, p. 223 (Russian). | Zbl 0499.14013

[39] V. E. Voskresenskiĭ, A. A. Klyachko, Toroidal Fano varieties and root system, Math. USSR Izvestija, 24 (1985), 221-244. | Zbl 0572.14029

[40] A. Weil, Algebras with involutions and the classical groups, J. Indian Math. Soc., 24 (1960), 589-623. | MR 25 #147 | Zbl 0109.02101

[41] A. Weil, Adèles and algebraic groups, Inst. for Adv. Study, Princeton, 1964.

[42] V. I. Yanchevskiĭ, Reduced norms of simple algebras over function fields, Proc. Steklov Inst. Math., 183 (1991), 261-269. | MR 92a:11143 | Zbl 0736.16010